Best Known (45, 45+38, s)-Nets in Base 2
(45, 45+38, 34)-Net over F2 — Constructive and digital
Digital (45, 83, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(45, 45+38, 121)-Net in Base 2 — Upper bound on s
There is no (45, 83, 122)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(283, 122, S2, 38), but
- the linear programming bound shows that M ≥ 2 969418 532036 180477 484353 208562 221056 / 265014 591075 > 283 [i]